Nearly three in four New Yorkers say the city is doing too little to help the homeless — and a majority disapprove of the way Mayor Bill de Blasio is handling the problem.

But that’s not stopping the City Council from moving full speed ahead on legislation to back away from police enforcement of crimes so often seen among the street homeless, like urinating and drinking alcohol in public.

Speaker Melissa Mark-Viverito is determined to undo the highly successful “broken windows” policing policy that has played such a key role in driving crime down to record low levels.

A package of eight bills to be introduced at the council Monday would steer even more “low-level” non-violent crimes to civil proceedings, where fines would replace jail sentences.

But those minor crimes, and others like turnstile-jumping, have often proved to be precursors to more serious offenses.

Broken windows gets thugs — and, often, their illegal guns — off the streets before they “graduate” to more serious crimes.

It’s the difference between preventing crimes before they occur and stepping in only after crimes have been committed.

And it comes as a new Quinnipiac University poll shows continued public discontent over the growing homeless crisis — and what New Yorkers see as the downward spiral of the city’s quality of life.

Fully 73 percent said City Hall needs to do more to help the homeless, and 55 percent say the mayor is mishandling poverty and homelessness — despite his recent initiative aimed at responding more quickly.

In fact, 58 percent said they see more homeless people on the streets these days.

Obviously, there’s a direct connection between how seriously the city takes quality-of-life crimes and New York’s actual quality of life — which nearly half of those questioned say has gotten worse in recent years.

Keeping New York safe and livable takes hard work and effective policing. Yet the council is headed in the opposite direction.